Multichannel calculation of excited vector $\varphi$ resonances and the $\varphi (2170)$

Abstract

A multichannel calculation of excited $J^{PC}=1^{--}$ $\varphi$ states is carried out within a generalization of the Resonance-Spectrum Expansion, which may shed light on the classification of the $\varphi (2170)$ resonance, discovered by BABAR and originally denoted X(2175). In this framework, a complete spectrum of bare $s\bar{s}$ states is coupled to those OZI-allowed decay channels that should be most relevant for the considered energy range. The included $S$- and $P$-wave two-meson channels comprise the lowest pseudoscalar, vector, scalar, and axial-vector mesons, while in the $q\bar{q}$ sector both the ${}^3{S}_1$ and ${}^3{D}_1$ states are coupled. The only two free parameters are tuned so as to reproduce mass and width of the $\varphi (1020)$, but come out reasonably close to previously used values. Among the model's $T$-matrix poles, there are good candidates for observed resonances, as well other ones that should exist according to the quark model. Besides the expected resonances as unitarized confinement states, a dynamical resonance pole is found at $(2186-i246)$ MeV. The huge width makes its interpretation as the $\varphi (2170)$ somewhat dubious, but further improvements of the model may change this conclusion.

Comments: 6 pages, 5 figures, RevTex4; v2: very recent experimental result, some extra discussion, and 2 references added; v3: 3 new figures, 2 new equations, and some rephrasing; version accepted for publication in Phys. Rev. D